Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 11 - Additional Topics - 11.5 - Quadratic Equations: Complex Solutions - Problem Set 11.5: 17

Answer

{$2-4i,2+4i$}

Work Step by Step

Step 1: Comparing $x^{2}-4x+20=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we find: $a=1$, $b=-4$ and $c=20$ Step 2: The quadratic formula is: $x=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$ Step 3: Substituting the values of a, b and c in the formula: $x=\frac{-(-4) \pm \sqrt {(-4)^{2}-4(1)(20)}}{2(1)}$ Step 4: $x=\frac{4 \pm \sqrt {16-80}}{2}$ Step 5: $x=\frac{4 \pm \sqrt {-64}}{2}$ Step 6: $x=\frac{4 \pm \sqrt {-1\times64}}{2}$ Step 7: $x=\frac{4 \pm (\sqrt {-1}\times\sqrt {64})}{2}$ Step 8: $x=\frac{4 \pm (i\times 8)}{2}$ Step 9: $x=\frac{4 \pm i(8)}{2}$ Step 10: $x=\frac{2(2 \pm 4i)}{2}$ Step 11: $x=2 \pm 4i$ Step 12: $x=2+4i$ or $x=2-4i$ Step 13: Therefore, the solution set is {$2-4i,2+4i$}.
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